Hybrid vehicle technology has been disclosed in Japanese Patent Provisional Publication No. 2001-263383 (hereinafter is referred to as “JP2001-263383”). In JP2001-263383, a hybrid vehicle is disclosed having a first clutch that connects and disconnects an engine and a motor, a second clutch that connects and disconnects the motor and drive road wheels, and a transmission. This hybrid vehicle employs a motor drive mode in which the first clutch is released and the vehicle travels by using only the motor as a power source. Also employed is an engine-used drive mode in which the first clutch is engaged and the vehicle travels while including the engine as the power source. When changing the mode from the motor drive mode to the engine-used drive mode, the first clutch is engaged, and a motor torque is increased and applied to the engine to start the engine. Thus, while in the motor drive mode, a margin for the motor torque is required to be secured to accommodate the increase in the motor torque for starting the engine. Here, when a vehicle travels at an extremely low speed, such as a low engine rotational speed (rpm) that is less than a minimum engine rpm required to allow self-rotation of the engine even when selecting a lowest transmission ratio (for instance, a low or first speed) including at an engine start, the self-rotation of the engine is allowed by slipping the second clutch. That is, by slipping the second clutch, while the drive road wheels are being rotated by the motor at an extremely low revolution speed, the engine is rotated at a rpm which allows the self-rotation of the engine.